Paper Dictionaries (etc) I like:

Oxford Advanced Learners Dictionary of American English — finally in a U.S. edition, the OALD is impressive for its scope, research background, and new list of the essential 3000 words of English (the Oxford 3000).

Collins COBUILD Advanced Dictionary of American English — the first U.S. edition of this very influential learner’s dictionary. I really like this book — it has lots of examples, usage notes, and thesaurus notes.

The Oxford Learner’s Thesaurus — an unusual but useful reference: combines a thesaurus (synonyms) with definitions, lots of information about correct usage, and collocations (words/phrases that go together). Comes with a CD-ROM for your computer.

The learners dictionaries from Oxford and Cambridge are also very good.